Integrate the following functions with respect to x: x2+2x+10

Question

Integrate the following functions with respect to x:

`sqrt(x^2 + 2x + 10)`

Sum

Solution

`int sqrt(x^2 + 2x + 10) "d"x = int sqrt((x + 1)^2 + 1^2 + 10) "d"x`

= `int sqrt((x + 1)^2 + 9) "d"x`

= `int sqrt((x + 1)^2 + 3^2) "d"x`

Put x + 1 = t

dx = dt

= `int sqrt("t"^2 + 3^2) "dt"`

= `"t"/2 sqrt("t" + 3^2) + 3^2/2 log |"t" + sqrt("t"^2 + 3^2)| + "c"`

= `"t"/2 sqrt("t"^2 + 3^2) + 3^2/2 log |"t" + sqrt("t"^2 + 3^2)| + "c"`

= `((x + 1))/2 sqrt((x + 1)^2 + 3^2) + 3^2/2 log |x + 1 sqrt((x + 1)^2 + 9)| + "c"`

= `((x + 1))/2 sqrt(x^2 + 2x 1 + 9) + 9/2 log |x + 1 + sqrt(x^2 + 2x + 1 + 9)| + "c"`

= `((x + 1))/2 sqrt(x^2 + 2x + 10) + 9/2 log |x + 1 + sqrt(x^2 + 2x + 10)| + "c"`

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Indefinite Integration with Standard Indefinite Integral Formulae - Methods of Integration

Is there an error in this question or solution?

Q 1. (i)Q 2. (iii)Q 1. (ii)

Chapter 11: Integral Calculus - Exercise 11.12 [Page 225]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board

Chapter 11 Integral Calculus
Exercise 11.12 | Q 1. (i) | Page 225

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